How to eas buid ios app to selected provider?

I am developer and have a apple developer account. I am now developing an app for a client so I have helped them create their own apple developer account made me a admin user so I can publish apps to the their account.

I searched extensively on how to do a eas build in this siutation.

At one point eas build asks for a provider and I select my clients account but the bundle identifier is registered on my account instead. So that is one problem.

Can the bundleidentifier be regisetered on my account? But that doesnt work when i try to submit the build?

I have tried getting my client to create the app and bundleidentifer on their account and then how do I build and submit to their app on their account?

Plz help im lost?